Question

f(x) = \(\sqrt{9-x^2}\). Find the domain of the function.

(a) (0,3)

(b) [0,3]

(c) [-3,3]

(d) (-3,3)

This question was posed to me by my college professor while I was bunking the class.

My query is from Functions topic in section Relations and Functions of Mathematics – Class 11

Answer 1

Right option is (c) [-3,3]

To explain: We know radical cannot be negative. So, 9-x,^2 ≥ 0

(3-x) (3+x) ≥ 0 => (x-3) (x+3) ≤ 0 => x∈[-3,3].